I had one that was difficult to seal although the original had been good for 15 years. I found the "cultured marble" was rough in the seal area. I sanded it ; 50 or 80 grit , just to take out bumps, nothing fancy . Then the putty and rubber held fine. Apparently the original plumber used a lot of putty and torque.
Plumbers putty (or appropriate alternative) is to be used under the drain trim flange at the top of the assembly, to seal the drain at the sink bowl. NOT at the bottom.
The bottom of the drain assembly should seal to the bottom sink hole by use of a tapered rubber gasket, no putty.
So I was able to remove the cap by using 2 channel lock pliers and some strips of rubber I cut from a sheet of rubber. The rubber was used to help me grip the cap and the faucet without doing TOO much damage to it from the pliers' teeth.
I gripped the faucet to hold it steady with 1 channel lock plier and used another to grip and turn the cap off. Easy-...